An Analysis of Asynchronous Stochastic Accelerated Coordinate Descent

TL;DR

This paper demonstrates that asynchronous parallel acceleration can be effectively combined with coordinate descent, achieving linear and sublinear speedups for convex and strongly convex functions under bounded asynchrony.

Contribution

It provides the first analysis of asynchronous parallel accelerated coordinate descent, showing how acceleration and parallelism can be combined effectively.

Findings

Linear speedup for strongly convex functions with limited asynchrony.

Sublinear speedup for strongly convex functions with larger asynchrony.

Sublinear speedup for general convex functions.

Abstract

Gradient descent, and coordinate descent in particular, are core tools in machine learning and elsewhere. Large problem instances are common. To help solve them, two orthogonal approaches are known: acceleration and parallelism. In this work, we ask whether they can be used simultaneously. The answer is "yes". More specifically, we consider an asynchronous parallel version of the accelerated coordinate descent algorithm proposed and analyzed by Lin, Liu and Xiao (SIOPT'15). We give an analysis based on the efficient implementation of this algorithm. The only constraint is a standard bounded asynchrony assumption, namely that each update can overlap with at most q others. (q is at most the number of processors times the ratio in the lengths of the longest and shortest updates.) We obtain the following three results: 1. A linear speedup for strongly convex functions so long as q is not too large. 2. A substantial, albeit sublinear, speedup for strongly convex functions for larger q. 3. A substantial, albeit sublinear, speedup for convex functions.